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arXiv:2312.13187 · Physical Review A

Rotational states of an asymmetric vortex pair with mass imbalance in binary condensates

Alice Bellettini, Andrea Richaud, Vittorio Penna

Published May 1, 2024• 6 citations
arXivHTMLPDF

Abstract

We consider massive vortices in binary condensates, where the immiscibility condition entails the trapping of the minority component in the vortex cores of the majority component. We study such vortices by means of a two-dimensional pointlike model, and show how the relevant dynamical equations exhibit vortex-pair solutions characterized by different vortex masses and circular orbits of different radii $a$ and $b$. These solutions are validated by the simulations of the Gross-Pitaevskii equations for binary condensates. After examining the properties of the vortex-pair rotational frequency $\mathrm{\ensuremath{\Omega}}$ as a function of the vortex masses for a given pair geometry, we define the rotational-state diagram $\mathcal{D}$, describing all the possible vortex-pair solutions in terms of the orbit radii at given $\mathrm{\ensuremath{\Omega}}$. This includes solutions with equal-mass pairs but $a\ensuremath{\ne}b$ or with one of the two masses (or both) equal to zero. Also, we analytically find the minimum value of $\mathrm{\ensuremath{\Omega}}$ for the existence of such solutions, and obtain numerically the critical frequency ${\mathrm{\ensuremath{\Omega}}}_{c}$ below which $\mathcal{D}$ changes its structure and the transition to an unstable vortex-pair regime takes place. Our paper highlights an indirect measurement scheme to infer the vortex masses from the orbits' radii $a$ and $b$, and a link between the vortex masses and the vortex-pair small-oscillation properties.

DOI
10.1103/physreva.109.053301

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We consider massive vortices in binary condensates, where the immiscibility condition entails the trapping of the minority component in the vortex cores of the majority component. We study such vortices by means of a two-dimensional pointlike model, and show how the relevant dynamical equations exhibit vortex-pair solutions characterized by different vortex masses and circular orbits of different radii aaa and bbb. These solutions are validated by the simulations of the Gross-Pitaevskii equations for binary condensates. After examining the properties of the vortex-pair rotational frequency \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ as a function of the vortex masses for a given pair geometry, we define the rotational-state diagram D\mathcal{D}D, describing all the possible vortex-pair solutions in terms of the orbit radii at given \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ. This includes solutions with equal-mass pairs but a\ensuremath≠ba\ensuremath{\ne}ba\ensuremath=b or with one of the two masses (or both) equal to zero. Also, we analytically find the minimum value of \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ for the existence of such solutions, and obtain numerically the critical frequency \ensuremathΩc{\mathrm{\ensuremath{\Omega}}}_{c}\ensuremathΩc​ below which D\mathcal{D}D changes its structure and the transition to an unstable vortex-pair regime takes place. Our paper highlights an indirect measurement scheme to infer the vortex masses from the orbits' radii aaa and bbb, and a link between the vortex masses and the vortex-pair small-oscillation properties.
We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating boxlike circular trap, i.e., states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length, and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting.
© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the 'https://creativecommons.org/licenses/by/4.0/'Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.We consider the mean-field vortex solutions and their stability within a two-component Bose-Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantized vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation of the two-component vortex solution for a range of atom numbers of the infilling component by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the infilling component away from the center of the vortex core, thereby demonstrating their stability to small perturbations. Finally, we consider the dynamics of infilled vortices.
We study the massive point-vortex model introduced in Richaud et al. [A. Richaud, V. Penna, R. Mayol, and M. Guilleumas, Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.
We consider the mean-field vortex solutions and their stability within a two-component Bose-Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantized vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation of the two-component vortex solution for a range of atom numbers of the infilling component by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the infilling component away from the center of the vortex core, thereby demonstrating their stability to small perturbations. Finally, we consider the dynamics of infilled vortices. Published by the American Physical Society 2024
We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.
In this work, we consider vortex lattices in rotating Bose–Einstein condensates composed of two species of bosons having different masses. Previously (Barnett et al 2008 New J. Phys. 10 043030), it was claimed that the vortices of the two species form bound pairs and the two vortex lattices lock. Remarkably, the two condensates and the external drive all rotate at different speeds owing to the disparity of the masses of the constituent bosons. In this paper, we study the system by solving the full two-component Gross–Pitaevskii equations numerically. Using this approach, we verify the stability of the putative locked state that is found to exist within a disc centered on the axis of rotation and that depends on the mass ratio of the two bosons. We also derive a refined estimate for the locking radius tailored to the experimentally relevant case of a harmonic trap and show that this agrees with the numerical results. Finally, we analyze in detail the rotation rates of the different components in the locked and unlocked regimes.